Newbie question re lawn drainage
 

Hi new here so excuse any naivity! I have just dug up our 10x10 foot lawn as it wasn't doing very well which i blame on being watter logged. I basically think whoever put the lawn down originally just dumped soil from where they pt a patio area, increasing the lawn bed height by about 6 inches so i think it was just to deep. I beleive the soil is quite clay heavy from what ive read, causing the wet lawn under foot after a rain fall and in most of the winter months, although it does seem to dry over the summer. However the lawn is patchy and mossy. Anyway, i'm in the process of removing about 6 inches of soil from it which i'm half way through. Then i propose to lay new turf.

My question is one of drainage; i obviously dont want to turf it again for only the same problem to happen, and the lawn get soggy and have been looking at drainage. Most of the solutions talk about digging 3 foot deep trenches, laying drain pipes in a herring bone fashion for the water to drain off. however this seems like a lot of faff and overkill for such a small area! i think surely this advice is for far larger lawns?

I was wondering about just digging say two sloping trenches of about 6 inches wide and say a foot deep, filling them half with pea gravel, then topped over with soil. Would this suffice? Or do I really need to go down the whole buying perforated drain pipe root? I read somewhere this comes in 25 metre rolls which cant be right can it??!

Any advice?